Combining linear programming and principal-agent models: an example from environmental regulation in agriculture

The paper develops a methodology whereby a Principal-Agent model is combined with Linear Programming in order to deal with the design of environmental regulation in agriculture. Linear Programming is intended here mainly as a tool to estimate an agent's cost/profit function for the purpose of the Principal-Agent model. Two variants of the methodology are considered. First, agents' profit functions are estimated through the interpolation of the results of the parametrisation of the Linear Programming model. In the second option, relevant corner points of the discontinuous profit function generated by the parametrisation of the Linear Programming models are identified. These relevant corner points are then fed into a discrete-action Principal-Agent model. An exploratory application is provided, using a case study related to the purchase of environmental services from agriculture. The results show that Linear programming may represent a useful way to estimate cost/profit functions to feed Principal-Agent models as long as it allows to incorporate more information from the point of view of how decision making is carried out, particularly when the underlying agent's cost/profit function is generated by a bundle of different production activities. However, the choice of the specific procedure should be cautiously evaluated in order to fit the actual properties of the underlying production process. Also, particular attention should be placed on the manner in which constraints and technical coefficients affect the result of the downstream model.